Two identical silver spheres of mass m and radius r are placed a distance R (sphere 1) and 2R (sphere 2) from the sun respectively. The ratio of the gravitational force exerted by the sun on sphere 1 to the pressure of solar radiation on sphere 1 is T₁; the ratio for sphere 2 is T₂. The ratio of T₂ to T₁ is A) 0.25. B) 0.50. C) 1.0. D) 2.0. E) 4.0.

Question

Quizplus · Accepted Answer

The gravitational force exerted by the sun on a sphere is proportional to the mass of the sphere and inversely proportional to the square of the distance between the sphere and the sun. The pressure of solar radiation on a sphere is proportional to the surface area of the sphere and inversely proportional to the square of the distance between the sphere and the sun. The ratio of the gravitational force to the pressure of solar radiation is therefore proportional to the ratio of the mass of the sphere to its surface area. Since the two spheres are identical, the ratio of their masses to their surface areas is the same. Therefore, the ratio of T2 to T1 is 1.

Two Identical Silver Spheres of Mass M and Radius R